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SPLP: A Certifiably Globally Optimal Solution to the Relative Pose Estimation Problem Using Points and Line Pairs

JOURNAL OF INTERCONNECTION NETWORKS 2022年第SUPP02期22卷 2143045-2143045页

作者： Sun, Lei East China Univ Sci & Technol Sch Mech & Power Engn Shanghai 200237 Peoples R China

Estimating the relative pose between two calibrated views with 2d-to-2d correspondences is a fundamental problem in computer vision and 2d perception. In this paper, we present the first certifiably globally optimal solver that can simultaneously incorporate both points and lines as the non-minimal 2d-to-2d correspondences for this problem. Our first contribution is to derive a generalized polynomial-based objective function based on the geometric constraints of orthogonal and parallel line pairs. Built upon it, our second contribution is to reformulate the relative pose estimation problem as a constrained global optimization problem with a unified representation of both point and line pair correspondences. Our third contribution lies in relaxing this non-convex optimization problem to a convex Semi-definite Program (SdP) using Sum of Squares (SOS) relaxations so as to solve it via Gloptipoly 3 with a reliable guarantee of global optimality. In both synthetic and real experiments, we show that adopting line pairs as supplementary correspondences can greatly improve estimation accuracy, especially in the point-sparse situations, and that our solver, named SPLP (SOS-Point-and-Line-Pair), can outperform other state-of-the-art solvers.

关键词： Relative pose estimation 2d geometry Lasserre's hierarchy sum of squares

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GENERAL FORMULATION OF FUNCTIONAL EXPANSION TALLIES FOR REGULAR 2d GEOMETRIES IN SERPENT 2 MONTE CARLO COdE

GENERAL FORMULATION OF FUNCTIONAL EXPANSION TALLIES FOR REGU...

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2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

作者： Jambrina, Ana Leppänen, Jaakko LUT University P.O. Box 20 LappeenrantaFI-53851 Finland VTT Technical Research Centre of Finland Ltd. VTT P.O. Box 1000 FI-02044 Finland

ISBN: (纸本)9781713886310

This work generalises the application of functional expansion tallies to regular 2d and 3d geometries (derived from quadratic surfaces and extruded axially), based on orthogonal 2d polynomials in the unit disc. Zernike polynomials, as a special case of Jacobi polynomials, are selected as a basis for the analysis. The study describes the construction of the completeness set of polynomials based on an on-the-fly geometry-variable transformation methodology and particularises the approach to circle partitions and deformations. The results are evaluated against pre-calculated polynomials basis sets derived from Gram-Schmidt orthogonalisation process and bin-based reference solution. Copyright © 2021 AMERICAN NUCLEAR SOCIETY, INCORPORATEd, LA GRANGE PARK, ILLINOIS *** rights reserved.

关键词： 2d geometry functional expansion tallies Monte Carlo Serpent 2 Zernike polynomials

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Testing convexity of figures under the uniform distribution

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RANdOM STRUCTURES & ALGORITHMS 2019年第3期54卷 413-443页

作者： Berman, Piotr Murzabulatov, Meiram Raskhodnikova, Sofya Penn State Univ Dept Comp Sci & Engn University Pk PA 16802 USA Boston Univ Dept Comp Sci 111 Cummington St Boston MA 02215 USA

We consider the following basic geometric problem: Given epsilon is an element of(0,1/2), a 2-dimensional black-and-white figure is SMALL ELEMENT OF- far from convex if it differs in at least an SMALL ELEMENT OF fraction of the area from every figure where the black object is convex. How many uniform and independent samples from a figure that is SMALL ELEMENT OF- far from convex are needed to detect a violation of convexity with constant probability? This question arises in the context of designing property testers for convexity. We show that Theta(epsilon-4/3) uniform samples (and the same running time) are necessary and sufficient for detecting a violation of convexity in an SMALL ELEMENT OF-far figure and, equivalently, for testing convexity of figures with 1-sided error. Our algorithm beats the omega(epsilon-3/2) lower bound by Schmeltz [32] on the number of samples required for learning convex figures under the uniform distribution. It demonstrates that, with uniform samples, we can check if a set is approximately convex much faster than we can find an approximate representation of a convex set.

关键词： Convex sets 2d geometry property testing randomized algorithms

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Preconditioning full-waveform inversion with efficient local correlation operators

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GEOPHYSICS 2019年第3期84卷 R321-R332页

作者： Wellington, Paul Brossier, Romain Virieux, Jean Univ Grenoble Alpes ISTerre Grenoble France Chevron Australia Perth WA Australia Univ Grenoble Alpes CNRS ISTerre Grenoble France

Full-waveform inversion (FWI) is an iterative locally linearized data-fitting technique. The FWI method attempts to move from an initial low-wavenumber representation of earth parameters to a broader representation of the medium. An issue with the method is that FWI is an ill-posed problem, oversampled for the numerical forward discretization. The success of the model parameter reconstruction can often be greatly affected by external factors such as the presence of noise in the input field data or other artifacts arising from the imaging condition present in the FWI gradient computation. We have developed a strategy for mitigating against the influence of such external factors by preconditioning the discrete data gradient using an efficient differential approach instead of the often used integral formulation. Such an application of a smoothing correlation operator allows one to use prior information to locally filter along expected geological dips while being consistent with faults. The application of this preconditioning strategy to real and synthetic 2d data sets illustrates how this incremental additional step makes the FWI workflow less sensitive to noise and spatial aliasing artifacts. Nothing prevents a possible 3d acoustic extension, thanks to the small added computer cost for this local filter application. Three-dimensional elastic FWI may require this inexpensive filtering strategy due to the prohibitive forward-modeling costs that could be partially mitigated by using a coarse shot increment in conjunction with gradient preconditioning.

关键词： FWI inversion preconditioning differential formulation 2d geometry prior information

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Synchronized forward-adjoint neutron transport using method of characteristics

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PROGRESS IN NUCLEAR ENERGY 2016年第0期92卷 211-219页

作者： Shokueifar, V. Zangian, M. Minuchehr, A. Zolfaghari, A. Shahid Beheshti Univ Dept Nucl Engn POB *** Tehran Iran

The method of characteristics has been widely used for neutron transport calculations in lattice physics computations. This method recently has attracted a lot of attention for whole core calculation because of its flexibility in geometry definition and to highly impose parallelization. One area of whole core calculation is perturbation calculation that needs forward-adjoint flux. The objective of the work presented in this paper is to develop a synchronized forward-adjoint neutron transport solver embedding in FAMOC code. FAMOC is a new neutron transport code based on method of characteristics that is currently under development at Shahid Beheshti University (SBU). It is capable of simulating 2d models based on combinatorial geometry with first or second-order surfaces, and a multilevel lattice-universe base geometry model to rectangularly simulate. In this code, the same tracking data is used to compute forward and adjoint average flux. The forward and adjoint effective multiplication factor, and flux obtained by FAMOC code for 2d benchmark of C5G7 were found to be in good agreement with references. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Multigroup neutron transport code Method of characteristics Forward-adjoint flux 2d geometry Lattice-universe base geometry model

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Numerical Solution of the Quantum Scattering Problem in the Plane

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PHYSICS OF PARTICLES ANd NUCLEI LETTERS 2015年第3期12卷 448-451页

作者： Koval, E. A. Koval, O. A. Melezhik, V. S. Joint Inst Nucl Res Bogoliubov Lab Theoret Phys Dubna 141980 Russia Dubna Int Univ Nat Soc & Man Dept Theoret Phys Dubna 141980 Russia

The algorithm for integration of the two-dimensional (2d) quantum scattering problem is developed. This approach was applied for investigation of anisotropy effects in 2d scattering. We have obtained good agreement of the numerical results with known asymptotics in a low-energy limit. It was found that the differential cross section depends weakly on the scattering angle in the low-energy limit for finite potentials, and the anisotropy of the potential causes angular features of the differential cross sections: at certain angles they have pronounced peaks.

关键词： modeling scattering of ultracold atoms 2d geometry optical traps

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Efficient Exciton Concentrators Built from Colloidal Core/Crown CdSe/CdS Semiconductor Nanoplatelets

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NANO LETTERS 2014年第1期14卷 207-213页

作者： Tessier, Mickael d. Spinicelli, Piernicola dupont, dorian Patriarche, Gilles Ithurria, Sandrine dubertret, Benoit Univ Paris 06 CNRS ESPCI Lab Phys & Etud Mat F-75005 Paris France CNRS Lab Photon & Nanostruct F-91460 Marcoussis France

We present the synthesis and the optical properties of a new type of two-dimensional heterostructure: core/crown CdSe/CdS nanoplatelets. They consist of CdSe nanoplatelets that are extended laterally with CdS. Both the CdSe core and the CdS crown dimensions can be controlled. Their thickness is controlled at the monolayer level. These novel nanoplatelet-based heterostructures have spectroscopic properties that can be similar to nanoplatelets or closer to quantum dots, depending on the CdSe core lateral size.

关键词： Nanoplatelets heterostructure nanosheets quantum wells 2d geometry fluorescence

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Spectroscopy of Colloidal Semiconductor Core/Shell Nanoplatelets with High Quantum Yield

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NANO LETTERS 2013年第7期13卷 3321-3328页

作者： Tessier, M. d. Mahler, B. Nadal, B. Heuclin, H. Pedetti, S. dubertret, B. Univ Paris 06 ESPCI CNRS Lab Phys & Etud Mat F-75005 Paris France

Free standing two-dimensional materials appear as a novel class of structures. Recently, the first colloidal two-dimensional heterostructures have been synthesized. These core/shell nanoplatelets are the first step toward colloidal quantum wells. Here, we study in detail the spectroscopic properties of this novel generation of colloidal nanoparticles. We show that core/shell CdSe/CdZnS nanoplatelets with 80% quantum yield can be obtained. The emission time trace of single core/shell nanoplatelets exhibits reduced blinking compared to core nanoplatelets with a two level emission time trace. At cryogenic temperatures, these nanoplatelets have a quantum yield close to 100% and a stable emission time trace. A solution of core/shell nanoplatelets has emission spectra with a full width half-maximum close to 20 nm, a value much lower than corresponding spherical or rod-shaped heterostructures. Using single particle spectroscopy, we show that the broadening of the emission spectra upon the shell deposition is not due to dispersity between particles but is related to an intrinsic increased exciton-phonon coupling in the shell. We also demonstrate that optical spectroscopy is a relevant tool to investigate the presence of traps induced by shell deposition. The spectroscopic properties of the core/shell nanoplatelets presented here strongly suggest that this new generation of objects will be an interesting alternative to spherical or rod-shaped nanocrystals.

关键词： Nanoplatelets nanosheets nanomembranes quantum wells 2d geometry heterostructure fluorescence

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Modelling of extended objects using sparse multi-aspect High Range Resolution radar data set

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IET RAdAR SONAR ANd NAVIGATION 2011年第7期5卷 756-768页

作者： Fasoula, A. van Genderen, P. Delft Univ Technol IRCTR MTS Radar Delft Netherlands

The two-dimensional (2d) geometry of extended objects is modelled as a discrete constellation of a small number of scattering centres. Each scattering centre is characterised by its 2d location and extension, as well as by its observability from aspect angles spanning a wide angular interval. The considered input information of the modelling consists of high range resolution (HRR) data sets, which are measured by a network of scanning surveillance radars from a limited set of aspect angles of the object. during the short time-on-target of the antennas within each radar scan, inverse synthetic aperture radar (ISAR) imaging is performed. The Expectation-Maximisation (ER) algorithm is applied in order to fit each ISAR image to a Gaussian mixture model (GMM), pertaining to the aspect angle applicable to the respective radar. A merging algorithm for clustering all the partial GMMs into a unique 2d model of the extended object is designed. Cluster validation criteria are applied for correct alignment of the multi-radar multi-scan object model estimates. A Mixture of Gaussians classifier (MOGC), which is based on representation of each object by the estimated 2d model, is discussed. Results from application of the algorithms to two measured HRR radar data sets are presented.

关键词： expectation-maximisation algorithm 2d geometry radar imaging ER algorithm sparse multiaspect high range resolution radar data set multiradar multiscan object model cluster validation criteria scanning surveillance radar Optical, image and video signal processing ISAR imaging MOGC discrete constellation Combinatorial mathematics Radar equipment, systems and applications search radar GMM HRR radar data set inverse synthetic aperture radar imaging Gaussian processes two-dimensional geometry synthetic aperture radar geometry Gaussian mixture model radar antennas wide angular interval antennas Other topics in statistics

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